There are nickel iron strings that are much brighter than Pressurewounds - Kalium makes some, for example. It's the geometry of the windings, not the alloy, that makes Pressurewounds sound different - there's more contact between layers than on a round wound, but less than a flat. My bet is that the alloy is chosen for pressurewounds because that metal crushes into an oval shape easily, not for its sonic character. If you doubt that it's the geometry that makes the difference, consider that most flats are made with stainless windings, and ...they're not at all bright.
As to the original question, as Pressurewounds pack more metal into a given diameter than a string with round windings, they take a bit more tension to get up to pitch than what a round of that diameter would - for similar tension, you want a smaller diameter string than you would normally use in a round.